Table 3.

Assumptions used in the model and possible improvements/extensions.

Assumption	Possible improvement/extension
Geometry and growth
• 1D tissue	• 2D and 3D tissue (Dyson et al., 2014)
• Homogeneous properties (cell shape, statoliths content, auxin carriers properties, and growth capabilities)	• Introducing a spatial variability (distribution) or inhomogeneity in cell and tissue properties
• Growth rate proportional to local auxin concentration	• More complex growth model coupled with
(Galston and Hand, 1949; Hopkins and Hüner, 2009)	the cell wall rheology (e.g., Dyson et al., 2014)
Auxin transport
• 1D transport (transverse gradient only, no longitudinal	• 2D and 3D auxin transport model
flux and gradient along the organ)	(e.g., Fendrych et al., 2018; Retzer et al., 2019)
• No production or degradation of auxin	• Adding auxin sink and source
(Kramer and Ackelsberg, 2015)
• Auxin concentration uniform in each cell and cell wall
(Kramer et al., 2007; Grieneisen et al., 2012)
• Continuum approximation: auxin gradients occurs on a	• Use of discrete (cellular) models
length scale larger than the cell size
• Coefficient of diffusion of auxin $\mathcal{D}$ not affected by PINs	• Use of the exact expression (9) in the algebra
polarization
PIN trafficking
• Conservation of PINs upon gravistimulation
(Kleine-Vehn et al., 2010; Rakusová et al., 2011)
• Statoliths modify PINs exocytosis (kon) and endocytosis	• See section 4.3
(koff) rate to favor cell membrane attachment ($\mathcal{R}>1$)
• PIN conductance α not affected by statoliths
• PINs diffusion inside the cell membrane neglected	• See section 4.3
(Kleine-Vehn et al., 2011)
• PINs bulk concentration uniform inside the cells	• Taking into account intracellular heterogeneities
	(vacuole, cytoskeleton, etc)
Statoliths dynamics
• Liquid behavior of the statoliths pile (horizontal free
surface in steady state) (Bérut et al., 2018)
• Neglect the duration of statoliths repositioning compared	• Add an equation for statoliths pile dynamics as in Chauvet et al. (2019)
to the gravitropic response time (Chauvet et al., 2019)
• Saltating (fluctuating) motion of statoliths neglected	• See section 4.2

References in the left column are those that support the assumptions; references in the right column are related to the proposed extensions.